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NIntegrate bug in Mathematica 6?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg84168] NIntegrate bug in Mathematica 6?
  • From: vlad <volodymyr.babich at gmail.com>
  • Date: Wed, 12 Dec 2007 05:12:50 -0500 (EST)

The following code in Mathematica 6:

Clear[logdist1, pdfLog1, \[Mu]1, \[Sigma]1]
logdist1 =
 LogNormalDistribution[(\[Mu]1 - \[Sigma]1^2/2), \[Sigma]1];
pdfLog1[x_] := PDF[logdist1, x]

\[Mu]1 = 0.05;
\[Sigma]1 = 0.2;

NIntegrate[Min[100, 100 b1]*pdfLog1[b1], {b1, 0, 5}]
NIntegrate[Min[100, 100 b1]*pdfLog1[b1], {b1, 0, 500}]
NIntegrate[Min[100, 100 b1]*pdfLog1[b1], {b1, 0, 10000}]
NIntegrate[Min[100, 100 b1]*pdfLog1[b1], {b1, 0, +\[Infinity]}]



Produces the following output:

94.1407

38.1789

38.1789

94.1407


Note that the first and the last integrals have upper bounds of 5 and
\
[Infinity]

The middle ones have bounds 500 and 10000

All of the answers should be the same (we are way in the tail of the
random variable density).  I get no warnings or errors.

Shouldn't Mathematica send me some warning that it has difficulty with
convergence?   Can I get Mathematica to send me a warning?   If not,
can I trust the numerical integration routines?

Incidentally, Mathematica 5.2 give the correct answer of 94.1407 in
all four cases.



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